Edge-choosability of multicircuits

Abstract

A multicircuit is a multigraph whose underlying simple graph is a circuit (a connected 2-regular graph). The List-Colouring Conjecture (LCC) is that every multigraph G has edge-choosability (list chromatic index) ch′( G) equal to its chromatic index χ′( G). In this paper the LCC is proved first for multicircuits, and then, building on results of Peterson and Woodall, for any multigraph G in which every block is bipartite or a multicircuit or has at most four vertices or has underlying simple graph of the form K 1, 1, p .